{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZG5B6LVZXKJCQKLCFCO7MOI7GL","short_pith_number":"pith:ZG5B6LVZ","canonical_record":{"source":{"id":"1511.01757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-05T14:21:56Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"c5683353bc920e2a3760d683b78d142e8cdf50f3f66423a4fcc4df9a704b0f8d","abstract_canon_sha256":"1f9b1db1233090b32d83e3584833fd73b0c79d160c73b3f6b7cd7fb0f1979ca6"},"schema_version":"1.0"},"canonical_sha256":"c9ba1f2eb9ba92282962289df6391f32d895bb9ba338681096b1add326c844a1","source":{"kind":"arxiv","id":"1511.01757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01757","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01757v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01757","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZG5B6LVZXKJC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZG5B6LVZXKJCQKLC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZG5B6LVZ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZG5B6LVZXKJCQKLCFCO7MOI7GL","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-05T14:21:56Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"c5683353bc920e2a3760d683b78d142e8cdf50f3f66423a4fcc4df9a704b0f8d","abstract_canon_sha256":"1f9b1db1233090b32d83e3584833fd73b0c79d160c73b3f6b7cd7fb0f1979ca6"},"schema_version":"1.0"},"canonical_sha256":"c9ba1f2eb9ba92282962289df6391f32d895bb9ba338681096b1add326c844a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:39.900922Z","signature_b64":"7LmdaCW/zaDjZ1SGjp7UzdocrxF1f8YlwRk0hqGEj0Puz5j4YycpxpISo2w6YErmOwpuh0G4YxeHf7gYJiZfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9ba1f2eb9ba92282962289df6391f32d895bb9ba338681096b1add326c844a1","last_reissued_at":"2026-05-18T01:27:39.900447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:39.900447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01757","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cpWe0BVuQu56njjkBTN+dYHmW8/LYUuM12yZwYztWM/OyLtj0tgouBKqLc46BC2rpoJPVNApHCDAbbBDAStGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:05:20.754124Z"},"content_sha256":"a2158a30f94ee07a9aab527948096a4444ad9c403cd340f7c6c9ae703fb7e59d","schema_version":"1.0","event_id":"sha256:a2158a30f94ee07a9aab527948096a4444ad9c403cd340f7c6c9ae703fb7e59d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZG5B6LVZXKJCQKLCFCO7MOI7GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge Invariance and Symmetry Breaking by Topology and Energy Gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Carlo Heissenberg, Franco Strocchi","submitted_at":"2015-11-05T14:21:56Z","abstract_excerpt":"For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\\mathcal A$, with a non-trivial center $\\mathcal Z$, describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations of $\\mathcal A$. In particular, this gives rise to a gauge symmetry described by the action of $\\mathcal Z$. A distinguished case is when the center of the observables arises from the fundamental group of the manifold of the positions of the quantum system. Symmetries which do not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01757","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JycwAG5snL3VK5fpSBa4pIkHSAGjsZ8FsNq4FysenfoNFAyPRXsFTE4j2/o4lq+0aUw8W8kECve5lJwJq+1tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:05:20.754859Z"},"content_sha256":"7f9b3265d1e9326041bb58f1d799ad4e768f8e82e6a187c1073e063c6459d6ed","schema_version":"1.0","event_id":"sha256:7f9b3265d1e9326041bb58f1d799ad4e768f8e82e6a187c1073e063c6459d6ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/bundle.json","state_url":"https://pith.science/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T00:05:20Z","links":{"resolver":"https://pith.science/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL","bundle":"https://pith.science/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/bundle.json","state":"https://pith.science/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZG5B6LVZXKJCQKLCFCO7MOI7GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZG5B6LVZXKJCQKLCFCO7MOI7GL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f9b1db1233090b32d83e3584833fd73b0c79d160c73b3f6b7cd7fb0f1979ca6","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-05T14:21:56Z","title_canon_sha256":"c5683353bc920e2a3760d683b78d142e8cdf50f3f66423a4fcc4df9a704b0f8d"},"schema_version":"1.0","source":{"id":"1511.01757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01757","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01757v1","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01757","created_at":"2026-05-18T01:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZG5B6LVZXKJC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZG5B6LVZXKJCQKLC","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZG5B6LVZ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:7f9b3265d1e9326041bb58f1d799ad4e768f8e82e6a187c1073e063c6459d6ed","target":"graph","created_at":"2026-05-18T01:27:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\\mathcal A$, with a non-trivial center $\\mathcal Z$, describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations of $\\mathcal A$. In particular, this gives rise to a gauge symmetry described by the action of $\\mathcal Z$. A distinguished case is when the center of the observables arises from the fundamental group of the manifold of the positions of the quantum system. Symmetries which do not","authors_text":"Carlo Heissenberg, Franco Strocchi","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-05T14:21:56Z","title":"Gauge Invariance and Symmetry Breaking by Topology and Energy Gap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01757","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a2158a30f94ee07a9aab527948096a4444ad9c403cd340f7c6c9ae703fb7e59d","target":"record","created_at":"2026-05-18T01:27:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f9b1db1233090b32d83e3584833fd73b0c79d160c73b3f6b7cd7fb0f1979ca6","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-05T14:21:56Z","title_canon_sha256":"c5683353bc920e2a3760d683b78d142e8cdf50f3f66423a4fcc4df9a704b0f8d"},"schema_version":"1.0","source":{"id":"1511.01757","kind":"arxiv","version":1}},"canonical_sha256":"c9ba1f2eb9ba92282962289df6391f32d895bb9ba338681096b1add326c844a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9ba1f2eb9ba92282962289df6391f32d895bb9ba338681096b1add326c844a1","first_computed_at":"2026-05-18T01:27:39.900447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:39.900447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7LmdaCW/zaDjZ1SGjp7UzdocrxF1f8YlwRk0hqGEj0Puz5j4YycpxpISo2w6YErmOwpuh0G4YxeHf7gYJiZfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:39.900922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2158a30f94ee07a9aab527948096a4444ad9c403cd340f7c6c9ae703fb7e59d","sha256:7f9b3265d1e9326041bb58f1d799ad4e768f8e82e6a187c1073e063c6459d6ed"],"state_sha256":"9a9abffd90c02b97aa58bed69f663366f825486bd97d16911d041fb94f7e32bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DidkSL8R99+w/u/v8P4tnYP1O8TO/VKA1vqenKgBPo06XgbClW5ql9dNb/GiY/u7FZDy6lNsmGUS/tNP6IIuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:05:20.758417Z","bundle_sha256":"dec5029a9b054e663c9e882ede687267d0ce90693d3153711694a54fd3e5c6cd"}}